Non-Gaussianities in the topological charge distribution of the SU(3) Yang-Mills theory

We present finite energy SU(2) Yang–Mills–Higgs particles of one-half topological charge. The magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole at the origin and a semi-infinite Dirac string on one-half of the z-axis carrying a magnetic flux of [Formula: see text] going into the origin. Hence the net magnetic charge is zero. The gauge potentials are singular along one-half of the z-axis, elsewhere they are regular.

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Large statistics study of QCD topological charge distribution

10.22323/1.032.0058 ◽

2006 ◽

Author(s):

Silvano Petrarca

Keyword(s):

Charge Distribution ◽

Topological Charge

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QUARKS AS TOPOLOGICAL DEFECTS — OR, WHAT IS CONFINED INSIDE A HADRON?

International Journal of Modern Physics A ◽

10.1142/s0217751x93002204 ◽

1993 ◽

Vol 08 (31) ◽

pp. 5575-5604 ◽

Cited By ~ 4

Author(s):

A. KOVNER ◽

B. ROSENSTEIN

Keyword(s):

Magnetic Flux ◽

Topological Charge ◽

Domain Walls ◽

Topological Defects ◽

Complex Scalar ◽

Yang Mills ◽

Effective Lagrangian ◽

Local Complex ◽

Complex Scalar Field ◽

The One

We present a picture of confinement based on representation of constituent quarks as pointlike topological defects. The topological charge carried by quarks and confined in hadrons is explicitly constructed in terms of Yang-Mills variables. In 2+1 dimensions we are able to construct a local complex scalar field V(x), in terms of which the topological charge is [Formula: see text]. The VEV of the field V in the confining phase is nonzero and the charge is the winding number corresponding to homotopy group π1(S1). Quarks carry the charge Q and therefore are topological solitons. The phase rotation of V is generated by the operator of magnetic flux. Unlike in QED, the U(1) magnetic flux is explicitly broken by the monopoles. This results in formation of a string between a quark and an antiquark. The effective Lagrangian for V is derived in models with adjoint and fundamental quarks. This topological mechanism of confinement is basically different from the one proposed by ’t Hooft in which the elementary objects are linelike domain walls. A baryon is described as a Y-shaped configuration of strings. In 3+1 dimensions the explicit expression for V, and therefore a detailed picture, is not available. However, assuming the validity of the same mechanism we point out several interesting qualitative consequences.

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Small instantons in weakly-gauged holographic models

Journal of High Energy Physics ◽

10.1007/jhep11(2021)136 ◽

2021 ◽

Vol 2021 (11) ◽

Author(s):

Tony Gherghetta ◽

Alex Pomarol

Keyword(s):

Topological Charge ◽

Conformal Transformation ◽

Analytic Solutions ◽

Strongly Coupled ◽

Yang Mills ◽

Interesting Class ◽

Gauge Couplings ◽

Topological Charges

Abstract Small instantons can play an important role in Yang-Mills theories whose gauge couplings are sizeable at small distances. An interesting class of theories where this could occur is in weakly-gauged holographic models (dual to Yang-Mills theories interacting with strongly-coupled CFTs), since gauge couplings are indeed enhanced towards the UV boundary of the 5D AdS space. However, contrary to expectations, we show that small instantons in these non-asymptotically-free models are highly suppressed and ineffective. This is due to the conservation of topological charge that forbids instantons to be localized near the UV boundary. Despite this fact we find non-trivial UV localized instanton-anti-instanton solutions of the Yang-Mills equations where the topological charges annihilate in the AdS bulk. These analytic solutions arise from a 5D conformal transformation of the uplifted 4D instanton. Our analysis therefore reveals unexpected nonperturbative configurations of Yang-Mills theories when they interact with strongly-coupled CFTs.

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Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09837-8 ◽

2021 ◽

Vol 81 (11) ◽

Author(s):

Fabrizio Canfora

Keyword(s):

Scalar Field ◽

Charge Density ◽

Topological Charge ◽

Conformal Symmetry ◽

Analytic Solutions ◽

Massless Scalar ◽

Massless Scalar Field ◽

Field Equations ◽

Yang Mills ◽

Non Linear

AbstractAn infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).

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Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptaa138 ◽

2020 ◽

Author(s):

Takuya Matsumoto ◽

Masakiyo Kitazawa ◽

Yasuhiro Kohno

Keyword(s):

Machine Learning ◽

Charge Density ◽

Topological Charge ◽

Dimensional Space ◽

Gradient Flow ◽

Fully Integrated ◽

Yang Mills ◽

Physical Volume ◽

Spatial Coordinates ◽

Small Flow

Abstract We apply a machine learning technique for identifying the topological charge of quantum gauge configurations in four-dimensional SU(3) Yang-Mills theory. The topological charge density measured on the original and smoothed gauge configurations with and without dimensional reduction is used for inputs of the neural networks (NN) with and without convolutional layers. The gradient flow is used for the smoothing of the gauge field. We find that the topological charge determined at a large flow time can be predicted with high accuracy from the data at small flow times by the trained NN; for example, the accuracy exceeds 99% with the data at t/a2 ≤ 0.3. High robustness against the change of simulation parameters is also confirmed with a fixed physical volume. We find that the best performance is obtained when the spatial coordinates of the topological charge density are fully integrated out as a preprocessing, which implies that our convolutional NN does not find characteristic structures in multi-dimensional space relevant for the determination of the topological charge.

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HALF-MONOPOLE AND MULTIMONOPOLE

International Journal of Modern Physics A ◽

10.1142/s0217751x05020811 ◽

2005 ◽

Vol 20 (10) ◽

pp. 2195-2204 ◽

Cited By ~ 6

Author(s):

ROSY TEH ◽

K. M. WONG

Keyword(s):

Natural Number ◽

Topological Charge ◽

Magnetic Charge ◽

Axially Symmetric ◽

Yang Mills ◽

First Order ◽

Half Integer

We would like to present some exact SU(2) Yang–Mills–Higgs monopole solutions of half-integer topological charge. These solutions can be just an isolated half-monopole or a multimonopole with topological magnetic charge ½m where m is a natural number. These static monopole solutions satisfy the first order Bogomol'nyi equations. The axially symmetric one-half monopole gauge potentials possess a Dirac-like string singularity along the negative z-axis. The multimonopole gauge potentials are also singular along the z-axis and possess only mirror symmetries.

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